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Zeration
#50
(07/05/2010, 12:00 AM)73939 Wrote: a o a=a+2

Though this is intuitive - because true for all operations [n] with n>0 on the left side - this is not true for zeration - if we require the following (mother) law to hold:

a [n+1] (x+1) = a [n] ( a [n+1] x )

which you already used on the left side for n=0, x=0; [0] is zeration, [1] is addition.

Actually not only *you* were confused about the failure of (*) a [n+1] m = a [n] ( a [n] ( ....( a[n]a ) ) ) - right side containing m times a - for n=0. But if one takes a close look one sees that one can only expect (from the mother law):
a [n+1] m = a [n] ( a [n] ( ... a [n] ( a [n+1] 1 ) ) ) ), where the right side contains m times a.

if now a [n+1] 1 = a (which is the case for all n>0) then (*) follows. But n=0 remains the exception, because a [0+1] 1 = a+1 != a.
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Messages In This Thread
Zeration - by GFR - 02/14/2008, 06:38 PM
RE: Zeration - by Ivars - 02/14/2008, 08:10 PM
RE: Zeration - by GFR - 02/14/2008, 10:41 PM
RE: Zeration - by mathamateur - 07/30/2009, 06:31 AM
RE: Zeration - by Ivars - 02/21/2008, 07:22 PM
RE: Zeration - by quickfur - 02/21/2008, 09:34 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:18 PM
RE: Zeration - by bo198214 - 02/21/2008, 10:25 PM
RE: Zeration - by quickfur - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:12 PM
RE: Zeration - by KAR - 02/21/2008, 11:04 PM
RE: Zeration - by quickfur - 02/21/2008, 11:52 PM
RE: Zeration - by GFR - 02/24/2008, 12:39 AM
RE: Zeration - by Ivars - 02/24/2008, 02:50 PM
RE: Zeration - by marraco - 03/20/2015, 09:59 PM
RE: Zeration - by bo198214 - 02/24/2008, 11:02 AM
RE: Zeration - by GFR - 03/19/2008, 12:40 PM
More on Zeration - by James Knight - 03/25/2008, 03:44 PM
Delta Numbers As HyperReals - by James Knight - 03/26/2008, 12:50 AM
RE: Delta Numbers As HyperReals - by Ivars - 03/26/2008, 12:15 PM
RE: Zeration - by GFR - 03/26/2008, 12:22 AM
RE: Zeration - by GFR - 04/05/2008, 08:58 PM
RE: Zeration - by Igor M - 01/14/2009, 04:04 PM
RE: Zeration - by bo198214 - 01/20/2009, 09:59 PM
RE: Zeration - by 73939 - 07/05/2010, 12:00 AM
RE: Zeration - by bo198214 - 07/05/2010, 07:37 AM
RE: Zeration - by brangelito - 07/20/2010, 05:51 PM
RE: Zeration - by bo198214 - 07/21/2010, 02:58 AM
RE: Zeration - by JmsNxn - 11/09/2011, 01:40 AM
RE: Zeration - by quickfur - 11/09/2011, 04:15 AM
RE: Zeration - by JmsNxn - 11/10/2011, 01:20 AM
RE: Zeration - by quickfur - 11/10/2011, 02:09 AM
RE: Zeration - by marraco - 03/20/2015, 09:44 AM
RE: Zeration - by marraco - 03/20/2015, 10:41 PM
RE: Zeration - by marraco - 03/21/2015, 12:35 AM
RE: Zeration - by marraco - 03/21/2015, 01:44 AM
RE: Zeration - by marraco - 03/21/2015, 04:10 AM
RE: Zeration - by MphLee - 03/21/2015, 11:53 AM
RE: Zeration - by marraco - 03/23/2015, 07:58 AM
RE: Zeration - by tommy1729 - 03/21/2015, 11:11 PM
RE: Zeration - by marraco - 03/23/2015, 08:05 AM
RE: Zeration - by marraco - 03/24/2015, 11:29 AM
RE: Zeration - by MphLee - 03/23/2015, 09:00 AM
RE: Zeration - by marraco - 03/23/2015, 01:39 PM
RE: Zeration - by MphLee - 03/23/2015, 02:31 PM
RE: Zeration - by Stanislav - 05/28/2015, 11:12 PM
RE: Zeration - by marraco - 05/29/2015, 01:33 AM
RE: Zeration - by Stanislav - 05/29/2015, 09:06 PM
RE: Zeration - by MphLee - 06/03/2015, 01:40 PM
RE: Zeration - by Stanislav - 06/04/2015, 06:44 AM
RE: Zeration - by marraco - 06/04/2015, 08:44 PM
RE: Zeration - by MphLee - 06/05/2015, 09:10 PM
RE: Zeration - by Stanislav - 09/09/2015, 10:04 PM
RE: Zeration - by Stanislav - 10/31/2016, 02:57 PM

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